Numerical solution of a fuzzy system of linear equations with polynomial parametric form

A systems of linear equations are used in many fields of science and industry, such as control theory and image processing, and solving a fuzzy linear system of equations is now a necessity. In this work we try to solve a fuzzy system of linear equations having fuzzy coefficients and crisp variables using a polynomial parametric form of fuzzy numbers.     

Modified iterative methods for nonnegative matrices and M-matrices linear systems

The purpose of this paper is to present new preconditioning techniques for solving nonnegative matrices linear system and M-matrices linear system Ax = b based on the I + S(α) type preconditioning matrices provided by Hadjidimos et al. ^[1] and Evans et al. ^[2]. Convergence analysis of the proposed methods are given. Numerical results are presented, which show the improvements on the convergence rate of the Jacobi type and Gauss-Seidel type preconditioned iterative methods.     

Parallel,iterative solution of sparse linear systems: Models and architectures

Solving large, sparse, linear systems of equations is a fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication.The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.     

Numerical solution of a system of fuzzy polynomials by fuzzy neural network

In this paper, a new approach for solving systems of fuzzy polynomials based on fuzzy neural network (FNN) is presented. This method can also lead to improve numerical methods. In this work, an architecture of fuzzy neural networks is also proposed to find a real root of a system of fuzzy polynomials (if exists) by introducing a learning algorithm. Finally, we illustrate our approach by numerical examples.     

Parallel algorithms for the solution of certain large sparse linear systems

A couple of approximate inversion techniques are presented which provide a parallel enhancement to several iterative methods for solving linear systems arising from the discretization of boundary value problems. In particular, the Jacobi, Gauss‐Seidel, and successive overrelaxation methods can be improved substantially in a parallel environment by the extensions considered. A special case convergence proof is presented. The use of our approximate inverses with the preconditioned conjugate gradient method is examined and comparisons are made with some recently proposed algorithms in this area that also employ approximate inverses. The methods considered are compared under sequential and parallel hardware assumptions.     

线性模糊微分系统的同伦摄动法

利用模糊结构元方法,将线性模糊微分系统转换成同解的线性确定微分系统。采用同伦摄动法给出线性确定微分系统的近似解,进而给出原模糊微分系统的近似解。给出了具体算例。     

基于模糊线性回归的脑卒中发病率预测模型

针对经典线性回归模型不能完全反映变量间的耦合关系而不适宜有模糊数的脑卒中发病率预测的问题,建立了一种模糊多元线性回归分析的脑卒中发病率预测模型。把历史数据分为建模数据样本和检测数据样本,采用线性规划法求出参数的中心值和模糊幅度值。实验结果表明,该模型具有较高的精确度和可操作性。     

Numerical solutions for linear system of first-order fuzzy differential equations with fuzzy constant coefficients

In this paper, a novel iterative method is proposed to obtain approximate-analytical solutions for the linear systems of first-order fuzzy differential equations (FDEs) with fuzzy constant coefficients (FCCs) while avoiding the complexities of eigen-value computations. A theorem for the convergence and the validity of the approach is also presented in detail. Numerical experiments and comparisons with exact solutions reveal that the proposed method is capable of generating accurate results.     

Perturbation analysis of fuzzy linear systems

This paper deals with the perturbation analysis of fuzzy linear systems. Three cases of perturbation are considered: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged, and (c) both the coefficient matrix and the right hand side are perturbed. For all of the three cases, the respective relative error bounds for solutions of fuzzy linear system are derived. The results are illustrated by numerical examples.     

Generalized tridiagonal preconditioners for solving linear systems

The paper presents a type of tridiagonal preconditioners for solving linear system Ax=b with nonsingular M-matrix A, and obtains some important convergent theorems about preconditioned Jacobi and Gauss–Seidel type iterative methods. The main results theoretically prove that the tridiagonal preconditioners cannot only accelerate the convergence of iterations, but also generalize some known results.     

A new iterative refinement of the solution of ill-conditioned linear system of equations

In this paper, a new iterative refinement of the solution of an ill-conditioned linear system of equations are given. The convergence properties of the method are studied. Some numerical experiments of the method are given and compared with that of two of the available methods.     

A weight space-based approach to fuzzy multiple-objective linear programming

In this paper, the effects of uncertainty on multiple-objective linear programming models are studied using the concepts of fuzzy set theory. The proposed interactive decision support system is based on the interactive exploration of the weight space. The comparative analysis of indifference regions on the various weight spaces (which vary according to intervals of values of the satisfaction degree of objective functions and constraints) enables to study the stability and evolution of the basis that correspond to the calculated efficient solutions with changes of some model parameters.     

A new identification method for fuzzy linear models of nonlinear dynamic systems

The most promising methods for identifying a fuzzy model are data clustering, cluster merging and subsequent projection of the clusters on the input variable space. This article proposes to modify this procedure by adding a cluster rotation step, and a method for the direct calculation of the consequence parameters of the fuzzy linear model. These two additional steps make the model identification procedure more accurate and limits the loss of information during the identification procedure. The proposed method has been tested on a nonlinear first order model and a nonlinear model of a bioreactor and results are very promising.     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

Robust solution of the linear servomechanism problem

This paper furnishes a solution to the problem of designing robust controllers for linear servomechanisms. The results complete the work begun by Pearson et al. in that a general class of exogenous signals is included in the problem formulation.     

Polyhedral representation of fuzzy linear bases

 In [15], we introduced the concepts of fuzzy bases, fuzzy linear interpolation and fuzzy polygon of four-component fuzzy linear bases. In [16], these concepts were used in the maximal profile of the set of polygons generated from a set of break points for each variable dimension. Theconcept was operationalized in a fuzzy linear basis algorithm (FLBA) for nonlinear separable programming problems involving no more than a finite number of discontinuities. The FLBA provides a powerful platform forparallel processing of the fuzzy linear sub-problems included in the finite FLB-chain. In this paper we extend the theory of fuzzy linear bases from the set of polygons toapolyhedral representation of four-component fuzzy linear bases defined on a closed subset of the real line.     

基于灰色GM(1,N)的模糊多元线性回归分析及应用

建立了基于对称三角模糊数的多元线性回归分析模型(简记为F L R模型),利用线性规划求出中心值和模糊度。以我国1995年到2008年粮食产量(来自《中国统计年鉴2009》)为原始数据,进行了多因素模糊拟合分析。利用GM(1,N)模型对2009年至2013年影响我国粮食产量的5个因素指标值进行了预测,将预测值代入FLR模型求出年度粮食产量,并与2009和2010年的实际产量比较,表明这种GM(1,N)模型和FLR模型有机结合形成的复合模型,预测精度高,可操作性强,且具有很高的可信度。     

三角模糊数直觉模糊Bonferroni平均算子及其应用

针对决策信息为三角模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出了一种基于三角模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法。首先,基于TFNIFN的运算法则和Bonferroni平均(BM)算子,定义了三角模糊数直觉模糊BM算子和TFNIFWBM算子;然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的MAGDM模型,结合排序方法进行决策。最后通过MAGDM算例验证了该算子的有效性与可行性。     

Fuzzy entropy in fuzzy weighted linear regression model under linear restrictions with simulation study

In fuzzy set theory, it is well known that a fuzzy number can be uniquely determined through its position and entropy. Hence, by using the concept of fuzzy entropy the estimators of the fuzzy regression coefficients may be estimated. In the present communication, a fuzzy linear regression (FLR) model with some restrictions in the form of prior information has been considered. The estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted/unrestricted FLR model by assigning some weights in the distance function. Some numerical examples have also been provided in order to illustrate the proposed model along with the obtained weighted estimators. Further, in order to compare the performance of unrestricted estimator and restricted estimator, a simulation study has been conducted by using two fundamental criteria of dominance – mean squared error matrix (MSEM) and absolute bias.